Multiplication of Two Numbers Using Circles: A Visual Geometric Method

① This GeoGebra example demonstrates a novel way to multiply two numbers by drawing circles and counting intersection points, turning arithmetic multiplication into a visual geometric construction. ② The core mathematical concepts involve multiplication, geometric construction, and the relationship between number operations and circle-line intersections, incorporating elements like points, segments, midpoints, perpendicular lines, and angles. ③ Construction details: Based on the summary, the example uses GeoGebra commands such as Point, Segment, Midpoint, Circle, OrthogonalLine, Angle, Intersect, and LineBisector, with objects including a, b, A, B, AB, C, BC, O, circle1, e, Ga, D, E, F, EF, G, CG, h, Gb, H, circle2, I, BI, value, and text1, enabling dynamic interaction and real-time visualization. ④ This resource is suitable for middle school students (around grades 7-8) learning multiplication concepts, introductory geometric construction, or for teachers to demonstrate in class and for students to explore independently, fostering a deeper understanding of how multiplication can be represented geometrically.